For a given magnification at the sensor plane and a given aperture, DoF is ~ identical.--Ceterum censeo soleam calidam ISO esse delendam.

Your "~" is key here. It's close, but not identical. What appears to be making the impact is that the circle of confusion is slightly smaller on an APS-C than a Full Frame, by .01mm.

At very close distances from lens to subject, the difference will be small. But as you get further away from your subject, the depth of field differences grows bigger and bigger.

For Example:

APS with 50mm (75mm equivalent) at F/2.8:

At 1ft, the DoF is .01ft

At 5ft, the DoF is .33ft

At 10ft, the DoF is 1.36ft

At 50ft, the DoF is 39ft

Full Frame with 75mm (75mm equivalent) at F/2.8:

At 1ft, the DoF is .01ft

At 5ft, the DoF is .22ft

At 10ft, the DoF is .9ft

At 50ft, the DoF is 24.1ft

Notice how as the distance from lens to subject increases, how the depth of field on the APS-C becomes greater than the Full Frame?

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Paul

With same (or wider) FOV, FF will have the ability to better isolate. But when we tend to disregard FOV and want it to be as narrow as possible, crop sensors end up with the edge. For example, at about 30 ft, Minolta 200/2.8 would have a DOF of 8" with APS-C but 12" on FF, because now the lens is actually providing a wider FOV. A 300/2.8 on FF, of course would match the FOV of 200/2.8 on APS-C, and will have a shallower DOF.